Fundamental Solution of a Quasistatic Problem for a Half Space with Two-Dimensional Discontinuities

We propose a method for the solution of a three-dimensional problem of determination of displacements in a half space within the framework of the theory of elasticity. The wave field of displacements induced by the formation of discontinuities in the body and loads specified on the surface of the half space is represented in the form of a double-layer potential of the theory of elasticity. The fundamental solution of the problem is obtained for the case where the time dependences of the loads and opening displacements of discontinuities are described by a harmonic law.